Combined Exponential-Type Estimators for Finite Population Mean in Two-Phase Sampling

A family of exponential-type estimator for estimating population mean in two-phase sampling when the population proportion of the auxiliary character is available is proposed in this paper. Theoretically, the bias and minimum mean square error (MSE) for the proposed estimator are obtained. The expression for MSE of the proposed exponential-type of estimator is compared with the existing estimators in the literature. The optimum values of the parameters are determined. An empirical study was carried out by comparing the proposed estimators with some of the existing estimators reviewed in the literature based on the criteria of bias, mean square error (MSE) and relative efficiency using life datasets. The result of the comparisons showed that the proposed exponential-type estimators produce a better estimate of finite population mean than the existing estimators in the sense of having higher percentage relative efficiency which implies lesser mean square error and bias. Furthermore, the realistic conditions under which the proposed class of exponential-type estimators is more efficient were also presented. Thus, the proposed estimators can be considered as significant alternatives to estimating population characteristics of real life datasets.